Abstract
We combine two partons on a random lattice as a vector state. In the ladder approximation, we find that such states have 1/p2 propagators (after tuning the mass to vanish). We also construct some diagrams which are very similar to 3-string vertices in string field theory for the first oscillator mode. Attaching 3 such lattice states to these vertices, we get Yang–Mills and F3 interactions up to 3-point as from bosonic string (field) theory. This gives another view of a gauge field as a bound state in a theory whose only fundamental fields are scalars.
Highlights
It is known that, in nonrelativistic quantum mechanics, Regge behavior relates the angular momenta and energies of bound states [1]
The BetheSalpeter equation [2] takes the place of the Schrodinger equation, which can only be solved in certain approximations, such as the ladder approximation or a perturbative Feynman diagram analysis
The Feynman diagrams of the particles underlying this bosonic string were studied and linear Regge trajectories were reproduced in the ladder approximation [5]
Summary
In nonrelativistic quantum mechanics, Regge behavior relates the angular momenta and energies of bound states [1]. The Feynman diagrams of the particles underlying this bosonic string were studied and linear Regge trajectories were reproduced in the ladder approximation [5] This implies that the only fundamental fields are scalars and all others can be represented as composite fields. The outline of this article is: section 2, a brief review of Reggy theory; section 3, a review of the bosonic lattice string; section 4, reproducing linear Regge trajectories in the ladder approximation; section 5, introducing the new massless external state from the lattice; section 6, constructing two simple 3-state interacting diagrams on the lattice, computing the 3-point interactions similar to the usual Yang-Mills field; section 7, comparing the two 3-state vertices with Witten’s vertex and the CaneschiSchwimmer-Veneziano (CSV) vertex in string field theory; and section 8, discussions
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